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A Decision Analysis Framework for High-fidelity and Low-fidelity Systems with Applications in Manufacturing Processes

Fan Zhang, Qiong Zhang, Madhura Limaye, Dhanashree Shinde, Gang Li, Sai Aditya Pradeep, Srikanth Pilla

TL;DR

A decision analysis framework based on multi-fidelity Gaussian process (GP) modeling based on the Kennedy-O'Hagan (KOH) framework is developed that integrates information from both high-fidelity and low-fidelity data sources to support decision-making under parameter uncertainty.

Abstract

Optimizing complex manufacturing processes often involves a trade-off between data accuracy and acquisition cost. High-fidelity data are accurate but limited, while low-fidelity data are abundant but often biased. Balancing these two sources is critical for efficient manufacturing optimization. To address this challenge, we develop a decision analysis framework based on multi-fidelity Gaussian process (GP) modeling based on the Kennedy-O'Hagan (KOH) framework. We propose a systematic Bayesian calibration approach using multi-fidelity GPs that explicitly quantifies the model discrepancy, and an algorithm that combines posterior sampling of calibration parameters with predictive sampling to characterize the distribution of optimal input settings and their associated uncertainty. These components are integrated into a five-stage practical workflow for the optimization of manufacturing processes. Through an illustrative example and two real-world applications in composite cure cycle optimization and injection molding process control, we demonstrate how the framework integrates information from both high-fidelity and low-fidelity data sources to support decision-making under parameter uncertainty.

A Decision Analysis Framework for High-fidelity and Low-fidelity Systems with Applications in Manufacturing Processes

TL;DR

A decision analysis framework based on multi-fidelity Gaussian process (GP) modeling based on the Kennedy-O'Hagan (KOH) framework is developed that integrates information from both high-fidelity and low-fidelity data sources to support decision-making under parameter uncertainty.

Abstract

Optimizing complex manufacturing processes often involves a trade-off between data accuracy and acquisition cost. High-fidelity data are accurate but limited, while low-fidelity data are abundant but often biased. Balancing these two sources is critical for efficient manufacturing optimization. To address this challenge, we develop a decision analysis framework based on multi-fidelity Gaussian process (GP) modeling based on the Kennedy-O'Hagan (KOH) framework. We propose a systematic Bayesian calibration approach using multi-fidelity GPs that explicitly quantifies the model discrepancy, and an algorithm that combines posterior sampling of calibration parameters with predictive sampling to characterize the distribution of optimal input settings and their associated uncertainty. These components are integrated into a five-stage practical workflow for the optimization of manufacturing processes. Through an illustrative example and two real-world applications in composite cure cycle optimization and injection molding process control, we demonstrate how the framework integrates information from both high-fidelity and low-fidelity data sources to support decision-making under parameter uncertainty.
Paper Structure (18 sections, 26 equations, 7 figures, 1 table, 1 algorithm)

This paper contains 18 sections, 26 equations, 7 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and Motivation
  3. Related Literature
  4. Our Contribution
  5. Problem Overview
  6. Multi-fidelity Bayesian Calibration: Modeling, Estimation, and Prediction
  7. Joint Gaussian Process Model
  8. Parameter Estimation
  9. Posterior Predictive Distribution
  10. Decision Analysis
  11. Illustrative Example
  12. Data Generation
  13. Parameter Estimation Results
  14. Decision Analysis
  15. Robustness
  16. ...and 3 more sections

Figures (7)

  • Figure 1: Decision Analysis Framework for High-fidelity and Low-fidelity Systems
  • Figure 2: Distribution of minima locations obtained by optimizing the GP emulator fitted only to the low-fidelity data.
  • Figure 3: Distribution of minima locations obtained by optimizing the GP model fitted only to the sparse high-fidelity observations.
  • Figure 4: Distribution of minima locations obtained by applying Bayesian calibration to both low-fidelity data and high-fidelity observations.
  • Figure 5: The distributions of MSE values across the 50 datasets.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Example 1
  • Example 2